Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

A unified approach to combinatorial key predistribution schemes for sensor networks

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

There have been numerous recent proposals for key predistribution schemes for wireless sensor networks based on various types of combinatorial structures such as designs and codes. Many of these schemes have very similar properties and are analysed in a similar manner. We seek to provide a unified framework to study these kinds of schemes. To do so, we define a new, general class of designs, termed “partially balanced t-designs”, that is sufficiently general that it encompasses almost all of the designs that have been proposed for combinatorial key predistribution schemes. However, this new class of designs still has sufficient structure that we are able to derive general formulas for the metrics of the resulting key predistribution schemes. These metrics can be evaluated for a particular scheme simply by substituting appropriate parameters of the underlying combinatorial structure into our general formulas. We also compare various classes of schemes based on different designs, and point out that some existing proposed schemes are in fact identical, even though their descriptions may seem different. We believe that our general framework should facilitate the analysis of proposals for combinatorial key predistribution schemes and their comparison with existing schemes, and also allow researchers to easily evaluate which scheme or schemes present the best combination of performance metrics for a given application scenario.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bag S., Saha A., Sarkar P.: Highly resilient key predistribution scheme using transversal designs and Reed Muller codes for wireless sensor network. In: CNSA, 2011. CCIS, vol. 196, pp. 344–355 (2011).

  2. Blackburn S.R., Etzion T., Martin K.M., Paterson M.B.: Efficient key predistribution for grid-based wireless sensor networks. In: ICITS, 2008. Lecture Notes in Computer Science, vol. 5155, pp. 64–69 (2008).

  3. Blackburn S.R., Etzion T., Martin K.M., Paterson M.B.: Distinct-difference configurations: multihop paths and key predistribution in sensor networks. IEEE Trans. Inf. Theory 56, 3961–3972 (2010)

    Article  MathSciNet  Google Scholar 

  4. Blanchard J.L.: A construction for orthogonal arrays with strength t ≥ 3. Discret. Math. 137, 35–44 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  5. Blom R.: An optimal class of symmetric key generation systems. In: EUROCRYPT, 1984. Lecture Notes in Computer Science, vol. 209, pp. 335–338 (1985).

  6. Blundo C., De Santis A., Herzberg A., Kutten S., Vaccaro U., Yung M.: Perfectly secure key distribution for dynamic conferences. Inf. Comput. 146, 1–23 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  7. Bose M., Dey A., Mukerjee R.: Key predistribution schemes for distributed sensor networks via block designs. Des. Codes Cryptogr. doi:10.1007/s10623-011-9590-1.

  8. Bush K.A.: Orthogonal arrays of index unity. Ann. Math. Stat. 23, 426–43 (1952)

    Google Scholar 

  9. Çamtepe S., Yener B.: Combinatorial design of key distribution mechanisms for wireless sensor networks. In: ESORICS, 2004. Lecture Notes in Computer Science, vol. 3193, pp. 293–308 (2004).

  10. Çamtepe S., Yener B.: Key distribution mechanisms for wireless sensor networks: a survey. Technical Report TR-05-07. Rensselaer Polytechnic Institute (2005).

  11. Çamtepe S., Yener B.: Combinatorial design of key distribution mechanisms for wireless sensor networks. IEEE/ACM Trans. Netw. 15, 346–358 (2007)

    Article  Google Scholar 

  12. Chakrabarti D., Maitra S., Roy B.: A key pre-distribution scheme for wireless sensor networks: merging blocks in combinatorial design. In: ISC, 2005. Lecture Notes in Computer Science, vol. 3650, pp. 89–103 (2005).

  13. Chakrabarti D., Maitra S., Roy B.: A hybrid design of key pre-distribution scheme for wireless sensor networks. In: ICISS, 2005. Lecture Notes in Computer Science, vol. 3803, pp. 228–238 (2005).

  14. Chakrabarti D., Seberry J.: Combinatorial structures for design of wireless sensor networks. In: ACNS, 2006. Lecture Notes in Computer Science, vol. 3989, pp. 365–374 (2006).

  15. Chan H., Perrig A., Song D.: Random key predistribution schemes for sensor networks. In: Proceedings of the 2003 symposium on security and privacy. IEEE Computer Society, pp. 197–213.

  16. Chen C.-Y., Chao H.-C.: A survey of key predistribution in wireless sensor networks. Secur. Commun. Netw., to appear (published online, July 13, 2011).

  17. Colbourn, C.J., Dinitz, J.H. (eds): Handbook of Combinatorial Designs, 2nd edn. Chapman & Hall/CRC, London (2007)

    MATH  Google Scholar 

  18. Dhar A., Sarkar P.: Full communication in a wireless sensor network by merging blocks of a key predistribution using Reed Solomon codes. In: CCSAE, 2011. CS & IT, vol. 2, pp. 389–400 (2011).

  19. Dong J.-W., Pei D.-Y., Wang X.-L.: A class of key predistribution schemes based on orthogonal arrays. J. Comput. Sci. Technol. 23, 825–831 (2008)

    Article  MathSciNet  Google Scholar 

  20. Dong J.-W., Pei D.-Y., Wang X.-L.: A key predistribution scheme based on 3-designs. In: Inscrypt, 2007. Lecture Notes in Computer Science, vol. 4990, pp. 81–92 (2008).

  21. Du W., Deng J., Han Y., Varshney P., Katz J., Khalili A.: A pairwise key predistribution scheme for wireless sensor networks. ACM Trans. Inf. Syst. Secur. 8, 228–258 (2005)

    Article  Google Scholar 

  22. Eschenauer L., Gligor V.: A key-management scheme for distributed sensor networks. In: Proceedings of the 9th ACM conference on computer and communications security. ACM Press, pp. 41–47 (2002).

  23. Hanani H.: A class of three-designs. J. Comb. Theory A 26, 1–19 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  24. Huffman W.C., Pless V.: Fundamentals of Error-Correcting Codes. Cambridge University Press, Cambridge (2003)

    Book  MATH  Google Scholar 

  25. Lee J., Stinson D.R.: Deterministic key predistribution schemes for distributed sensor networks. In: SAC, 2004. Lecture Notes in Computer Science, vol. 3357, pp. 294–307 (2005).

  26. Lee J., Stinson D.R.: A combinatorial approach to key predistribution for distributed sensor networks. In: IEEE Wireless Communications and Networking Conference (WCNC 2005), vol. 2, pp. 1200–1205.

  27. Lee J., Stinson D.R.: On the construction of practical key predistribution schemes for distributed sensor networks using combinatorial designs. Technical Report CACR 2005-40, Centre for Applied Cryptographic Research, University of Waterloo (2005). http://www.cacr.math.uwaterloo.ca/techreports/2005/cacr2005-40.pdf.

  28. Lee J., Stinson D.R.: Common intersection designs. J. Comb. Des. 14, 251–269 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  29. Lee J., Stinson D.R.: On the construction of practical key predistribution schemes for distributed sensor networks using combinatorial designs. ACM Trans. Inf. Syst. Secur. 11(2), article No. 1 (2008).

    Google Scholar 

  30. Liu D., Ning P., Li R.: Establishing pairwise keys in distributed sensor networks. ACM Trans. Inf. Syst. Secur. 8, 41–77 (2005)

    Article  Google Scholar 

  31. Martin K.M.: Discrete Structures in the Theory of Secret Sharing, PhD thesis, University of London (1991).

  32. Martin K.M.: On the applicability of combinatorial designs to key predistribution for wireless sensor networks. In: IWCC, 2009. Lecture Notes in Computer Science, vol. 5557, pp. 124–145 (2009).

  33. Martin K.M.: The rise and fall and rise of combinatorial key predistribution. In: SAC, 2010. Lecture Notes in Computer Science, vol. 6544, pp. 92–98 (2011).

  34. Martin K.M., Paterson M.B., Stinson D.R.: Key predistribution for homogeneous wireless sensor networks with group deployment of nodes. ACM Trans. Sens. Netw. 7(2), article No. 11 (2010).

    Google Scholar 

  35. Mitra S., Dutta R., Mukhopadhyay S.: A hierarchical deterministic key pre-distribution for WSN using projective planes. In: ADHOCNETS, 2011. LNICST, vol. 89, pp. 16–31 (2012).

  36. Payne S.E., Thas J.A.: Finite Generalized Quadrangles, 2nd edn. European Mathematical Society Publishing House, Zürich (2009).

  37. Pei D.-Y.: Authentication Codes and Combinatorial Designs. Chapman & Hall/CRC, Boca Raton (2006)

    MATH  Google Scholar 

  38. Pei D.-Y., Dong J.-W., Rong C.M.: A novel key predistribution scheme for wireless distributed sensor networks. Sci. China Inf. Sci. 53, 288–298 (2010)

    Article  MathSciNet  Google Scholar 

  39. Ruj S., Roy B.: Key predistribution schemes using partially balanced designs in wireless sensor networks. In: ISPA, 2007. Lecture Notes in Computer Science, vol. 4742, pp. 431–445 (2007).

  40. Ruj S., Roy B.: Key predistribution schemes using codes in wireless sensor networks. In: Inscrypt, 2008. Lecture Notes in Computer Science, vol. 5487, pp. 275–288. Beijing, China (2008).

  41. Ruj S., Roy B.: Revisiting key predistribution using transversal designs for a grid-based deployment scheme. Int. J. Distrib. Sens. Netw. 5, 660–674 (2008)

    Article  Google Scholar 

  42. Ruj S., Roy B.: Key predistribution using combinatorial designs for a grid-group deployment scheme in wireless sensor networks. ACM Trans. Sens. Netw. 6(1), article No. 4 (2009).

    Google Scholar 

  43. Ruj S., Seberry J., Roy B.: Key predistribution schemes using block designs in wireless sensor networks. In: 2009 international conference on computational science and engineering, pp. 873–878.

  44. Sarkar P., Dhar A.: Assured full communication by merging blocks randomly in wireless sensor networks using Reed Solomon code for key predistribution. Int. J. Netw. Secur. Appl. 3, 203–215 (2011)

    Google Scholar 

  45. Sarkar P., Saha A., Bag S.: Security enhanced key predistribution scheme using transversal designs and Reed Muller codes for wireless sensor networks. Int. J. Netw. Secur. Appl. 3, 125–140 (2011)

    Google Scholar 

  46. Stinson D.R.: Combinatorial Designs, Constructions and Analysis. Springer, New York (2004)

    MATH  Google Scholar 

  47. van Lint J.H., Wilson R.M.: A Course in Combinatorics, 2nd edn. Cambridge University Press, Cambridge (2001)

    Book  MATH  Google Scholar 

  48. Wei R., Wu J.: Product construction of key distribution schemes for sensor networks. In: SAC, 2004. Lecture Notes in Computer Science, vol. 3357, pp. 280–293 (2004).

  49. Xu L., Chen J., Wang X.: Cover-free family based efficient group key management strategy in wireless sensor network. J. Commun. 3, 51–58 (2008)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economics, Mathematics and Statistics, Birkbeck, University of London, Malet Street, London, WC1E 7HX, UK

    Maura B. Paterson

  2. David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Douglas R. Stinson

Authors
  1. Maura B. Paterson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Douglas R. Stinson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Douglas R. Stinson.

Additional information

Communicated by K. Matsuura.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Paterson, M.B., Stinson, D.R. A unified approach to combinatorial key predistribution schemes for sensor networks. Des. Codes Cryptogr. 71, 433–457 (2014). https://doi.org/10.1007/s10623-012-9749-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10623-012-9749-4

Keywords

Mathematics Subject Classification (2010)

Search

Navigation